Graca Carita University of E'vora Title: Dimensional reduction and relaxation for optimal design problems with a perimeter penalization

Abstract: A $3D-2D$ dimension reduction for a nonlinear optimal design problem with a perimeter penalization and with superlinear growth is performed providing an integral representation for the limit energy.

In the linear growth an integral representation in the space of functions of bounded variation is achieved. The presence of a perimeter penalization is also considered in order to avoid non existence of admissible solutions besides this leads to an interaction in the limit energy. More general models have been taken into account.